The acceleration of gravity on planet depend on its mass (M) and its size(R): g

Question

The acceleration of gravity on planet depend on its mass (M) and its size(R): g = GM/R^2 The constant G is Newton's gravitational constant, a number one can look up. But if we work in ratios, we don't have to care about any constants. Use algebra to show that the ratio g_M/g_E does not depend on G. Calculate the ratio of an astronaut's weight on Mars to their weight on Earth, W_M/W_E. Mars has a mass of 6.4 times 10^25 kg. while Earth has a larger mass 6.0 times 10^24 kg. The ratio of the radius of Earth to the radius of Mars is R_E/R_M = 1.89.

Explanation / Answer

here,

mass of Mars , Mm = 6.4 * 10^23 kg

mass of Earth , Me = 6 * 10^24 kg

the ratio ,R = Wm/We = gm /ge

R = ( G * Mm /Rm^2) /( G/Me /Re^2)

R = ( Mm /Me) * ( Re/Rm)^2

R = ( (6.4 * 10^23)/( 6 * 10^24)) * ( 1.89)^2

R = 0.38

the ratio of weight on Mars to the weight on earth is 0.38

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